As we saw in Chapter 6, the process of rounding a bit
vector often involves determining its degree of exactness. For this
purpose, therefore, it is also useful to predict the trailing
one of a sum, i.e., the least index at which a one occurs. The
following lemmas provide methods for computing, in constant time, an
integer that has precisely the same trailing one as the sum or
difference of two given operands.

Note that the difference
of
-bit vectors
and
is
commonly computed as a sum, using the identity
--
,
which leads to the formula

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Thus, we are also interested in computing the trailing one of an
incremented sum. This problem admits a particularly simple solution.